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Algebraic Geometric Comparison of Probability Distributions

Authors
Kiraly, Franz J.von Buenau, PaulMeinecke, Frank C.Blythe, Duncan A. J.Mueller, Klaus-Robert
Issue Date
3월-2012
Publisher
MICROTOME PUBL
Keywords
computational algebraic geometry; approximate algebra; unsupervised Learning
Citation
JOURNAL OF MACHINE LEARNING RESEARCH, v.13, pp.855 - 903
Indexed
SCIE
SCOPUS
Journal Title
JOURNAL OF MACHINE LEARNING RESEARCH
Volume
13
Start Page
855
End Page
903
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/105365
ISSN
1532-4435
Abstract
We propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of algebraic geometry, which we demonstrate in a compact proof for an identifiability criterion.
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